Hello

I have a many data points (intensity vs. wavelength). The signal is noisy so I would like to smooth it. The signal is also sumperimposed with another sinusodial function which I try to get rid of. There are some steps where I need you help.

First, here is my long list of data:

Fresnel1 = {{1.549`, 0.004039`}, {1.549002`, 
    0.0044009999999999995`}, {1.549004`, 0.003989`}, {1.549006`, 
    0.004048`}, {1.5490080000000002`, 
    0.0039840000000000006`}, {1.54901`, 
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    0.0037099999999999998`}, {1.549014`, 
    0.003989`}, {1.5490160000000002`, 0.003665`}, {1.549018`, 
    0.0035470000000000002`}, {1.54902`, 
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    0.0033299999999999996`}, {1.549026`, 
    0.0036339999999999996`}, {1.549028`, 0.0037`}, {1.54903`, 
    0.003268`}, {1.549032`, 
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    0.002851`}, {1.549036`, 0.002658`}, {1.5490380000000001`, 
    0.0028369999999999997`}, {1.54904`, 0.002932`}, {1.549042`, 
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    0.002906`}, {1.5490460000000001`, 0.002509`}, {1.549048`, 
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    0.002907`}, {1.5490540000000002`, 0.002761`}, {1.549056`, 
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As you can see the data is quite noisy and the signal is superimposed with another sinus:

Show[
 ListPlot[Fresnel1, AxesLabel -> {"wavelength [\[Mu]m]", "Intensity"}],
 ListLinePlot[Fresnel1, PlotStyle -> {Thin, PointSize[0.1]}, 
  AxesLabel -> {"wavelength [\[Mu]m]", "Intensity"}]
 ]

What I want to do is:

1.) Filter the sinus with smaller frequency out of my signal

2.) Smooth my signal by filtering the noise

As far as I understand the FFT I have to convert my signal from wavelength into frequency. Then I can apply the Mathematica functions Fourier[] and InverseFourier[] to filter my signal. But I think there is one important think to keep in mind and this is why I need your help.

If I convert the wavelength signal to frequency, the step size changes (is not equal anymore: delta lambda compared to delta frequency). And I have heard that this is important. First of all, is this actually correct? If yes, can you explain me why or where I can find more information about it? I think I have to define a wavelength array. How does this look like?

Fi = First[Dimensions [Fresnel1]];           
FresnelFrequency1 = 
  Table[{(3*10^8)/Fresnel1[[t, 1]]*10^6, Fresnel1[[t, 2]]}, {t, 
    Fi}];       

Show[
 ListPlot[FresnelFrequency1, 
  AxesLabel -> {"Frequency [Hz]", "Intensity"}],
 ListLinePlot[FresnelFrequency1, PlotStyle -> {Thin, PointSize[0.1]}, 
  AxesLabel -> {"Frequency [Hz]", "Intensity"}]
 ]

Because I think I have to deal with this sort of problem more often in the future, how would you solve step (1) and step (2) ?

Hope you can help me.

Peter